Did you know that the cheapest price per gram can still be the more expensive purchase for your family? A supermarket sign may announce “Buy two, get one free”. That sounds like an automatic bargain, but a pupil who calculates only the discount may miss an important question: how much of the food will actually be used?
A unit price is the amount paid per standard quantity, such as dollars per kilogram or per litre. To assess a multi-buy offer, calculate the whole amount paid, divide it by the total usable quantity received, and then check the quantity your household needs, the use-by period and any conditions on the offer. A lower unit price is a genuine mathematical comparison; it does not, on its own, make a larger purchase the right decision.
This is a lesson in education’s central purpose: carry a method from a worksheet into real judgment. We will compare exact quantities, test a misleading shortcut, practise independently and learn when the numbers are not enough.
An invented shopping example: three ways to buy the same ingredient
Imagine that a fictional shop sells identical plain oats in sealed packets. These are illustrative prices, not current supermarket offers. The ordinary packet contains 400 g for S$4.80. A promotion lets a shopper pay for two 400 g packets and take a third 400 g packet at no extra charge. A larger 750 g packet of the same oats costs S$6.75. Assume that pack weight is accurate, there are no extra charges, and all three options are comparable in quality.
- Ordinary packet: 400 g costs S$4.80, which is S$4.80 ÷ 0.4 kg = S$12.00 per kg.
- Multi-buy: pay 2 × S$4.80 = S$9.60 for 3 × 400 g = 1,200 g = 1.2 kg. Unit price = S$9.60 ÷ 1.2 kg = S$8.00 per kg.
- Larger packet: 750 g = 0.75 kg. Unit price = S$6.75 ÷ 0.75 kg = S$9.00 per kg.
The arithmetic checks both ways. At S$8 per kg, 1.2 kg costs S$9.60. At S$9 per kg, 0.75 kg costs S$6.75. A comparison based only on the large numeral “FREE” would not show these relationships.
The twist: the family needs only 600 g
Now add one realistic condition. The family needs 600 g this week and has no reliable way to keep surplus oats in acceptable condition after opening. The promotional purchase would require S$9.60 immediately, while the 750 g pack would require S$6.75 and cover the entire 600 g need. The 750 g pack is therefore S$2.85 cheaper in immediate spending, even though its price per kilogram is S$1 higher.
The promotional bundle could be sensible for someone who can safely use or store all 1.2 kg. For the household in this example it is not the least-cost way to meet the stated need. Do not confuse lowest unit price with lowest suitable total purchase. They answer different questions. Neither the example nor the comparison assumes that discarded food has a cash refund value.
Why a ‘free’ packet is not the same thing as free food for every shopper
A ‘buy two, get one free’ offer has a conditional price: the shopper must buy the required qualifying items. The third packet has no additional checkout price inside the bundle, but the buyer still has to commit to the first two. The offer can be described as a one-third reduction relative to buying three identical packets at the stated ordinary price: three would cost S$14.40, the bundle costs S$9.60, and the difference is S$4.80. S$4.80 ÷ S$14.40 = 1/3, or about 33.3%.
That 33.3% statement depends on the displayed regular price being the comparison base and on all three packets being eligible. Do not turn it into a claim about the buyer’s savings if the buyer would otherwise have bought only one packet, if a competing larger pack is cheaper, or if the promotion applies only to certain varieties.
A five-question diagnostic before doing the calculations
- What is the same measurable unit for every choice: packet, gram, kilogram or litre?
- How many items do I pay for, and how many do I receive?
- Does the offer apply to these sizes, flavours or dates? Are there purchase limits?
- What quantity will actually be used before it becomes unsuitable?
- Am I trying to minimise spending today, unit cost, or long-run cost?
If a learner cannot answer the first two questions, the unit-price calculation has not yet been set up. If they answer the first two but ignore the last three, the mathematics may be correct while the decision is poor. Different errors call for different corrections.
Progressive practice: model, pair, and independent choice
Guided problem: normalise every package to one kilogram
Write 400 g as 0.4 kg. Divide S$4.80 by 0.4, not by 400 if you intend to report dollars per kilogram. Write the unit next to the answer: S$12/kg. Then write 1,200 g as 1.2 kg and divide S$9.60 by 1.2. Compare S$12/kg and S$8/kg only after both describe the same quantity. A learner who writes S$0.012/g is also mathematically correct for the regular pack, but must convert it before comparing with another price per kilogram.
Shared problem: ask which decision the buyer is really making
A pair of pupils can role-play shoppers with different needs. Shopper A uses 1.2 kg over a fortnight and can store the packets. Shopper B needs 600 g only once. They should agree on the prices, then explain why they may choose different purchases. The purpose is not to argue that one person is better at arithmetic: it is to show how a constraint changes an otherwise shared calculation.
Independent transfer question with an answer check
A new fictional offer advertises three 250 g cartons of juice for S$4.50, while one 600 g carton of the same comparable product costs S$3.30. Which has the lower unit price? Three 250 g cartons total 750 g = 0.75 kg, so S$4.50 ÷ 0.75 = S$6.00/kg. The 600 g carton is 0.6 kg, so S$3.30 ÷ 0.6 = S$5.50/kg. The single larger carton has the lower unit price. A pupil must explain the decision in a full sentence and check whether weight is an appropriate comparison basis for the products in question. For drinks ordinarily priced by volume, actual labels should be compared in millilitres or litres instead; this fictional weight example is only arithmetic practice.
Misconceptions that deserve a specific repair
- “One packet is free, so the whole purchase is cheaper.” Repair: name the amount paid and the comparison bundle first.
- “The bigger total quantity must always win.” Repair: state the required amount, storage capacity and likely waste.
- “S$0.008 per gram and S$8 per kilogram are different deals.” Repair: 1,000 g equals 1 kg; multiply S$0.008/g by 1,000.
- “A percentage discount proves money saved.” Repair: distinguish the seller’s selected reference price from the buyer’s realistic alternative.
- “A good student must pick the promotion.” Repair: a justified refusal can show stronger quantitative reasoning than automatic acceptance.
What parents and teachers can observe
A parent can ask a child to photograph or copy two price labels with their quantities, then work out a fair comparison without buying anything. Avoid sharing other shoppers’ faces or private information. Let the child state a hypothetical household need and justify their choice. A teacher can provide four mock labels, vary only one condition at a time, and ask learners to revise the decision when the useable quantity changes.
Look for four observable improvements: the learner states the unit; calculates checkout totals separately from unit prices; identifies a condition such as shelf life; and checks the answer by reversing the calculation. Record these on a small two-week comparison sheet. A correct numerical answer without the decision rationale is partial progress, not complete transfer.
When this method has limits
Unit price can conceal differences in quality, concentration, nutritional value, packaging or usable portion. A cleaning liquid with a different dilution rate cannot automatically be compared by the shelf price per litre. For food with bones or shells, the purchased mass is not the same as the edible mass. Promotional terms may change; check the current label rather than treating the example as an actual offer.
Singapore’s Competition and Consumer Commission described unit pricing as a way to compare brands and pack sizes in its 27 August 2025 announcement about a supermarket pilot. Its price transparency guidance also discusses discounts and “free” claims. Those sources explain the consumer principle; they do not verify the invented prices above.
Frequently asked questions
Is buy-two-get-one-free always a 33.3% discount?
Only against the price of three identical qualifying items bought individually at the stated reference price, with no additional conditions changing the comparison. It is not a promise of 33.3% household savings.
What if the shopper can share the third item?
Include any actual sharing arrangement and cost split explicitly. If three friends take one packet each and pay equally, each share of the S$9.60 total is S$3.20. Do not silently assume that someone else will take or pay for the surplus.
Is it wrong to buy in bulk?
No. Bulk purchasing can be sensible when needs, storage, cash flow and product quality support it. The skill is to justify the purchase with the right comparison rather than with an advertising slogan.
What should a child write in a mathematics explanation?
“The bundle costs S$8 per kilogram, but we need only 600 g. The 750 g pack costs S$6.75 in total, compared with S$9.60 for the bundle, so I would choose the 750 g pack under the given storage condition.” That connects calculation and decision.
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This article belongs to the wider Education Hub. For another lesson about applying mathematical conditions to a real bill, read how to calculate parking charges with time blocks. For habits that turn procedures into independent judgment, see the immutable Secondary 1 Mathematics tutor Clementi guide. Good education is not merely noticing a bargain; it is knowing what the bargain means for the question you actually need to answer.